Is it possible that the face of the Sphinx is of Khufu (presuming that Khufu started to have the Sphinx built, during the final years of his reign) then Djedefra continued the building of the Sphinx or even perhaps prevented all process of the building of the Sphinx, until his reign ended and Khafra continued the building of the Sphinx during his reign until completed?

Explaining why the indentical dream stelea by Thutmosis IV mentioned both names of Khufu and Khafra..._________________It is of course the hieght of irony that, after this intensive campaign to expunge them from the annals of Egypt, the Amarna pharaohs are today probably the most recognized of all the country's ancient rulers!

The idea has been advanced that the Sphinx was carved/built during Khufu's reign and represents him... during Khafre's reign and represents him... during Khafre's reign and represents Khufu... and during Khufu's reign and represented him and was recarved to during Khafre's reign to represent him. (About the only combination I've not seen is 'carved during Khufu's reign to represent Khafre!')

I'm not sure that we can firmly settle this question with the data currently available. Until something comes along, I see no reason to depart from the majority opinion that it was carved during Khafre's reign, and therefore likely represents him (with just a slim chance he had it carved to resemble his father).

BTW, regarding Khafre carving the Sphinx to look like Khufu... one thing that strikes me is that Khufu's sons are the ones who went to using 'Re as part of their names... with the later possible example of Amenhotep III, I wonder if Khufu was deified as an incarnation of the sun during his lifetime, with his sons, etc., paying tribute to him in some fashion. This could be an impetus for carving the Sphinx to look like Khufu. However, this is pure speculation on my part.

I have little knowledge on this period of time in Ancient Egypt's history, my thoughts were originally (after watching an documentary about the Sphinx, released in 2008) that Khufu had designed a massive Sphinx to be built, with the face of himself, which had started construction during the end of Khufu's reign. Then Khafra in honor and tribute of his father continued and completed the Sphinx during his reign, with the original designs of his father face...

Theories go as far back as to say the Sphinx was originally a lion, which was altered by a later pharaoh, to depict the face of himself..._________________It is of course the hieght of irony that, after this intensive campaign to expunge them from the annals of Egypt, the Amarna pharaohs are today probably the most recognized of all the country's ancient rulers!

As far as I'm aware the Dream Stella only mentions 'Khaf...' and even that fragment of the name has flaked off now. It is the so-called 'Inventory Stela' which mentions Khufu as the restorer of the Sphinx. This stela is supposed to be a 26th Dynasty piece of historicism. Still it seems to reflect a tradition, existing in later times, that the Sphinx predates Khufu. This obviously contradicts the predominant view, i.e. that Khafre was the builder of the Sphinx.

"... Another stela dated to the 21st or 26th Dynasty (Wildung 1969, 182-4; Zivie 1980, 95) tells of ancient repairs to the Sphinx, specifically to the tail of the nemes headdress, and ascribes the repairs to Khufu, implying that the Sphinx precedes Khafre. This is the "Stela of Cheops's Daughter" [Cairo, JE 2091], discovered by Mariette in 1853 in the small Isis Temple east of the southernmost Queen's Pyramid at the foot of the Khufu Pyramid. The account is probably an example of the 'authenticating apparatus', an ancient literary device that bestows great antiquity on texts or monuments (Wilson 1950, 495), in this case on the Temple of Isis that is also said to have been restored by Khufu. ..."